The present invention relates to methods of image processing, and more particularly to methods for removing the degradation resulting from sampling systems where more than one channel of information is captured and both channel signal and sensitivity are unknown and vary at each sample location.
An example of a system that captures more than one channel with unknown and varying signal and sensitivity is a color filter array (CFA) film that has been spatially sampled with a film scanner. A CFA film for capturing the red, green, and blue channel information required for human color perception contains at least three colored species from which red, green, and blue channel information can be decoded. A CFA film can be designed for direct viewing and/or optical printing. However the CFA structure degrades image quality.
A CFA film is disclosed in EP 935168. The color filter array comprises colored resin particles which are randomly arranged.
If the number of independent channels of information acquired by electro-optical scanning of a CFA film is at least twice minus one the number of desired information channels, then at each scanned pixel location, it is possible to determine both the amount of signal (silver or other light modulating species formed in a photo process as a function of light intensity) formed in spatial coincidence with the total sub-pixel area occupied with similarly colored CFA elements (the relative sensitivity). The twice minus one arises from the area constraint at each pixel; that is that the sum of the area of all of the individual sub-pixel CFA elements is equal to the effective scanning aperture or pixel area. One such system is described in U.S. patent application Ser. No. 09/080,791 wherein twice the number of desired channels of independent information is acquired in order to essentially (within the limits of bit depth) determine both the amount of silver formed under the total sub-pixel area filled with similarly colored CFA elements and the total sub-pixel area filled with similarly colored CFA elements.
However, most existing scanning systems do not possess the capability of acquiring these extra channels of independent information required to perform this joint determination. By applying the following image processing method, it is possible to determine the amount of silver formed under the total sub-pixel area filled with similarly colored CFA elements and the total sub-pixel area filled with similarly colored CFA elements from electro-optical scanning where the number of independent channels of information acquired equals the number of desired information channels.
For a three channel system the problem to be solved, at each pixel position (p, q),
can be expressed as follows:
Cm1(p, q)=X1(p, q)C1(p, q)xe2x80x83xe2x80x83(1a)
Cm2(p, q)=X2(p, q)C2(p, q)xe2x80x83xe2x80x83(1b)
Cm3(p, q)=X3(p, q)C3(p, q)xe2x80x83xe2x80x83(1c)
X1(p, q)+X2(p, q)+X3(p, q)=1.0xe2x80x83xe2x80x83(1d)
where Cmi is the measured transmittance of the ith color channel, Xi 
is the fraction of effective scanning pixel area covered by sub-pixel CFA
elements of the ith color, and Ci is the desired recorded image signal for the ith channel at each pixel position (p, q). For simplification, the (p, q) will not be included explicitly in subsequent equations, but it will be understood that all equations are a function of pixel position.
A simple assumption would be that for each channel i in a local area, the average fraction of pixel area covered, the values of Xi, are constant and equal to the average fraction observed over the entire scanned image and these fractions are known. Defining these known fractions as {overscore (X)}i, and assuming that over some small area that essentially defines the window for a low pass filter, the values of Ci are calculated as follows:
xe2x80x83Ci=1pf(Cmi)/{overscore (X)}1 xe2x80x83xe2x80x83(2)
where 1pf(Cmi) is the low-pass version of the Cmi measurement, sufficiently low-passed so that the above average fraction assumption is constant. Low-pass filtering of a sampled image is well known in the art and is achieved, for example, by applying a finite impulse response (FIR) filter to a sampled signal.
Unfortunately, in order to achieve this constancy condition, excessive low-pass filtering is required, resulting in low spatial resolution and image quality. Alternate assumptions can be employed that result in improved image quality.
Another approach well-practiced in the art of color imaging is to transform the three measured signals, e.g. red, green, and blue, to signals such as one luminance and two chrominance signals. Luminance is broadly defined as a linear combination of red, green, and blue, all with positive weightings that sum to unity. The two chrominance signals are broadly defined as independent representations of the color information with weightings that sum to zero. A set of weightings that is used in television systems is:
L=0.30C1+0.59C2+0.11C3 xe2x80x83xe2x80x83(3a)
Bxe2x88x92L=xe2x88x920.30C1xe2x88x920.59C2+0.89C3 xe2x80x83xe2x80x83(3b)
Rxe2x88x92L=0.70C1xe2x88x920.59C2xe2x88x920.11C3 xe2x80x83xe2x80x83(3c)
where L is the luminance-like signal and B-L and R-L are the two chrominance-like signals. The weighting coefficients for L are all positive and sum to unity. The weighting coefficients for B-L and R-L sum to zero. For this example, C1=R (red), C2=G (green) and C3=B (blue). Owing to the characteristics of the human visual system, it is possible to low-pass filter chrominance signals significantly more than luminance signals whilst maintaining good image quality. Applying this transformation to the unknown signal, unknown sensitivity system described by equations (1) produces an improved image, i.e. an image without high frequency colored noise. The noise owing to the color filter array is reduced in some colored areas. However, most of the image suffers from CFA noise and colored mottle (low frequency color noise). The high frequency CFA noise is manifest as non-colored noise owing to the transformation, equation (3a), and lack of low-pass filtering of the L signal. If the CFA has low frequency power, then the resulting chrominance signals will contribute colored mottle (low frequency noise) to an image reconstructed after the above described image processing. If all of the transformed signals in equations (3) were equally low-pass filtered, then the result, by the application of linear systems theory, would be equivalent to that achieved by low-pass filtering the signals represented by equation (2).
It is an aim of the invention to provide a method of image processing which avoids the problems mentioned above, which does not require a special scanner but gives good quality results with typical scanning means.
According to the present invention there is provided a method of forming output signals from a plurality of channel input signals, said input signals being a function of both unknown recorded signal levels and unknown signal sensitivities, the method comprising the steps of;
sampling and measuring the product of the recorded signals and the signal sensitivities for each sampled channel input signal;
determining at each sampled location channel weighting values which eliminate the contribution of the unknown signal sensitivities; and
further processing the plurality of channel input signals using the determined channel weighting values to form output signals that represent the unknown recorded signal levels.
By applying multi channel scanning and image processing according to the invention it is possible to remove essentially all of the image quality degradation due to the CFA structure.